This article presents a new model of optical power gathered by a fiber-optic pyrometer when there is a tilting angle between the fiber longitudinal axis and the vector perpendicular to the tangent plane of the emitted surface. This optical power depends on the fiber specifications, such as the diameter and the numerical aperture (NA), as well as the object parameters, including its diameter, emissivity, and tilting angle. Some simulations are carried out using other pyrometers from the literature without tilting to validate the model. Additional simulations with different optical fibers, object sizes, and distances at different tilting angles allow us to describe the behavior of the pyrometer when the object is smaller than the optical fiber field of view (the light cone defined by its NA). The results show that for a finite surface object, the power collected by the optical fiber is affected by changes in the tilting angle, greater tilting lesser gathered power, and reaching the maximum power when the field of view of the fiber covers up the entire object, as expected. On the other hand, additional equations are presented to describe the maximum tilting angle, and distance that allow the maximum power gathered for a determined object diameter and fiber, avoiding temperature measurement errors.
Keywords: finite hot spot; modeling; optical fiber sensor; pyrometer; temperature; tilting angle.